Random walks are one approach for decentralized search in unstructured peer-to-peer (P2P) networks. In this search strategy, a
query is forwarded by each peer to a random neighbor. A replication strategy is then required to achieve a sufficiently high probability for finding requested data items. In this context, we investigate the problem to minimize the number of replicas needed to achieve a given availability constraint. An availability constraint is a minimum threshold for the probability to find an existing data item via random walks and can be specified for every data item and every peer. It turns out that this optimization problem can be formulated as a generalization of the partial set cover problem. Because of the NP-hardness of the
(partial) set cover problem, we use a greedy approximation algorithm to compute an optimal replica distribution and we investigate the worst-case approximation ratio of our algorithm. Finally, our goal is to develop a distributed replication algorithm that only requires local knowledge of the network.